Question

Use the average atomic masses given inside the front cover of this book to calculate the mass in grams of each of the following samples. a. 0.00552 mole of calcium b. 6.25 mmol of boron \((1 \mathrm{mmol}=1 / 1000 \mathrm{~mole})\) c. 135 moles of aluminum d. \(1.34 \times 10^{-7}\) moles of barium e. 2.79 moles of phosphorus f. 0.0000997 mole of arsenic

Short answer

a. 0.2212 g of Calcium b. 0.0676 g of Boron c. 3642.3 g of Aluminum d. \(1.84 \times 10^{-5}\) g of Barium e. 86.3063 g of Phosphorus f. 0.007479 g of Arsenic

Step-by-step solution

Identify the average atomic masses of elements

First, we need to locate the average atomic masses for Calcium (Ca), Boron (B), Aluminum (Al), Barium (Ba), Phosphorus (P), and Arsenic (As) from the reference source. The atomic masses are as follows: - Calcium (Ca): 40.08 g/mol - Boron (B): 10.81 g/mol - Aluminum (Al): 26.98 g/mol - Barium (Ba): 137.33 g/mol - Phosphorus (P): 30.97 g/mol - Arsenic (As): 74.92 g/mol

Calculate the mass in grams of each sample

Use the formula: mass (g) = moles × molar mass (g/mol) a. 0.00552 moles of Calcium: mass (g) = 0.00552 moles × 40.08 g/mol mass (g) = 0.2212 g b. 6.25 mmol of Boron: Convert mmol to moles: 6.25 mmol × (1/1000) = 0.00625 moles mass (g) = 0.00625 moles × 10.81 g/mol mass (g) = 0.0676 g c. 135 moles of Aluminum: mass (g) = 135 moles × 26.98 g/mol mass (g) = 3642.3 g d. \(1.34 \times 10^{-7}\) moles of Barium: mass (g) = \(1.34 \times 10^{-7}\) moles × 137.33 g/mol mass (g) = \(1.84 \times 10^{-5}\) g e. 2.79 moles of Phosphorus: mass (g) = 2.79 moles × 30.97 g/mol mass (g) = 86.3063 g f. 0.0000997 moles of Arsenic: mass (g) = 0.0000997 moles × 74.92 g/mol mass (g) = 0.007479 g

Key concepts

Molar Mass

Molar mass, one of the essential concepts in stoichiometry, represents the mass of one mole of a substance. It's expressed in grams per mole (g/mol). Understanding a substance's molar mass enables the conversion between the number of moles and mass in grams.

The molar mass can be determined using the atomic masses of the elements making up a compound. The atomic mass of each element can be found on the periodic table and is usually expressed as an average value due to isotopic variations. For instance, the molar mass of calcium is 40.08 g/mol, while aluminum's molar mass is 26.98 g/mol.

By knowing the molar mass, you can easily compute how much a particular quantity of moles would weigh. For example, with calcium's molar mass of 40.08 g/mol, you can determine the mass of any given amount of moles by multiplying these two values.

• Step 1: Identify the molar mass from a reliable reference or periodic table.
• Step 2: Confirm the value reflects the number of grams per mole (g/mol).

Moles to Grams Conversion

The conversion from moles to grams is a straightforward, yet crucial calculation in chemistry. This conversion hinges on the molar mass of the substance. Using the molar mass as a conversion factor, you can accurately calculate the mass of a given number of moles.

The formula used is: \[ \text{mass (g)} = \text{moles} \times \text{molar mass (g/mol)} \]. By multiplying the number of moles by the molar mass, you convert the amount into grams. This method is used universally for all elements and compounds, making it a versatile tool in stoichiometric calculations.

In practice, let's look at boron, an element with a molar mass of 10.81 g/mol. To find out the mass from 6.25 mmol (which is converted to 0.00625 moles from the millimoles), you multiply by the molar mass. This process gives you the precise mass in grams.

• Make sure to convert any units like millimoles to moles prior to calculating.
• Multiply the number of moles by the molar mass.

Atomic Mass

Atomic mass reflects the weighted average mass of an atom's isotopes, reflecting both the mass numbers and the relative abundance of each isotope. Typically measured in atomic mass units (amu), this measurement is pivotal when calculating molar masses.

While the atomic mass of an element is listed on the periodic table, it serves as a stepping stone to finding the molar mass when working with single elements. For elements like phosphorous and arsenic, their atomic masses directly inform the computations of their molar masses, helping in mass calculations of more complex compounds.

It is important to recognize that although atomic mass is dimensionless as a standalone number, it is fundamentally connected to the mol of an element when expressed as g/mol in molar mass calculations.

• Utilize the periodic table for accurate atomic masses.
• Remember, atomic mass is a cumulative average based on an element's isotopes.